Serpentine belt/tensioner questions

I just wanted to double-check to make sure I'm not being taken for a ride by an unfamiliar mechanic. Don't mean to offend, but I have had some terrible experiences in the past and can't afford a repeat.

My car's power-steering went out after heavy rain (and AC, etc.). This generally happens briefly during wet days, but instead of coming back right away like usual, it was continuously out. When I opened it up, my serpentine belt was entirely gone.

Everything else looks okay to me, but obviously I'm not a professional, so when they tell me the tensioner needs to be replaced, I am a bit confused. Is it possible that the rain, and not the part is the issue? Or is the moisture just aggravating the problems with my tensioner/s?

Also, how much should this cost, generally? I would really like the minimal amount of expense; I just need to be able to make the trip from MA to NJ so my gear-head brothers can deal with it.

Thank you very much for your time.